How do you prove that the line y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
If: y = 2x+5/4 and y^2 = 10x
Then: y^2 = (2x+5/4)^2
So: 4x^2 +5x +25/16 = 10x
Transposing terms: 4x^2 -5x +25/16 = 0
A line is tangent to a curve when the discriminant: b^2 -4ac =
0
Thus: 5^2 -4*4*25/16 = 0
Therefore: y = 2x+1.25 is a tangent to the curve y^2 = 10x